Background-Independent Gravitational Waves

TL;DR

This paper develops a background-independent approach to gravitational waves by linearizing tetrad gravity in a fixed gauge, providing explicit solutions to Einstein's equations without relying on a background spacetime.

Contribution

It introduces a Hamiltonian linearization method in a fixed gauge that yields explicit solutions for background-independent gravitational waves.

Findings

Explicit solutions to Hamiltonian constraints in tetrad gravity.

First linearized solutions of Einstein's equations in a background-independent context.

Description of gravitational waves in a well-defined post-Minkowskian space-time.

Abstract

A Hamiltonian linearization of the rest-frame instant form of tetrad gravity (gr-qc/0302084), where the Hamiltonian is the weak ADM energy ${\hat E}_{ADM}$, in a completely fixed (non harmonic) 3-orthogonal Hamiltonian gauge is defined. For the first time this allows to find an explicit solution of all the Hamiltonian constraints and an associated linearized solution of Einstein's equations. It corresponds to background-independent gravitational waves in a well defined post-Minkowskian Christodoulou-Klainermann space-time.